{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Runge-Kutta Numerical Scheme\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "u_i^{(1)} =&\\ u_i^{(n)} + \\frac{\\alpha \\Delta t}{\\Delta x^2} \\left( u_{i+1}^{(n)} - 2u_i^{(n)} + u_{i-1}^{(n)} \\right)\\\\\n",
    "u_i^{(2)} =&\\ \\frac{3}{4}u_i^{(n)} + \\frac{1}{4}u_i^{(1)} + \\frac{\\alpha \\Delta t}{4\\Delta x^2}\\left( u_{i+1}^{(1)} - 2u_i^{(1)} + u_{i-1}^{(1)} \\right)\\\\\n",
    "u_i^{(n+1)} =&\\ \\frac{1}{3}u_i^{(n)} + \\frac{2}{3}u_i^{(2)} + \\frac{2\\alpha \\Delta t}{3\\Delta x^2}\\left( u_{i+1}^{(2)} - 2u_i^{(2)} + u_{i-1}^{(2)} \\right)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_l, x_r, t = -1, 1, 1\n",
    "dx, dt = 0.025, 0.0025\n",
    "nx = int((x_r - x_l) / dx)\n",
    "nt = int(t / dt)\n",
    "\n",
    "alpha = 1 / np.pi**2\n",
    "beta = alpha * dt / dx**2\n",
    "\n",
    "u = np.zeros((nt + 1, nx + 1))\n",
    "x = np.linspace(x_l, x_r, nx+1)\n",
    "\n",
    "u[0, :] = -np.sin(np.pi*x, dtype=np.double)\n",
    "u[0, 0], u[0, -1] = 0, 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_1, u_2 = np.zeros(nx+1), np.zeros(nx+1)\n",
    "for i in range(1, nt+1):\n",
    "    for j in range(1, nx):\n",
    "        u_1[j] = u[i-1, j] + beta * (u[i-1, j+1] - 2 * u[i-1, j] + u[i-1, j-1])\n",
    "    for j in range(1, nx):\n",
    "        u_2[j] = 0.75 * u[i-1, j] + 0.25 * u_1[j] + 0.25 * beta * (u_1[j+1] - 2 * u_1[j] + u_1[j-1])\n",
    "    for j in range(1, nx):\n",
    "        u[i, j] = (1/3) * u[i-1, j] + (2/3) * u_2[j] + (2/3) * beta * (u_2[j+1] - 2 * u_2[j] + u_2[j-1])\n",
    "    u[i, 0], u[i, -1] = 0, 0\n",
    "u_ref = -np.exp(-t) * np.sin(np.pi * x)\n",
    "error = np.abs(u_ref - u[-1, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4), dpi=100)\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x, u_ref, \"k-\", linewidth=1.0, label=\"Solution\")\n",
    "plt.scatter(x, u[-1, :], facecolor=\"none\", edgecolor=\"blue\", s=20, linewidths=0.5, label=\"RK3\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"$u$\")\n",
    "plt.title(\"Solution field\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x, error, facecolor=\"none\", edgecolor=\"red\", s=20, linewidths=0.5)\n",
    "plt.ylabel(r\"$\\epsilon$\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.title(\"Discretization error\")\n",
    "plt.tight_layout()\n",
    "plt.ticklabel_format(axis='y', style='sci', scilimits=(-4,-4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gpytorch",
   "language": "python",
   "name": "gpytorch"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
